3 Answers
3

You may need basic tools for most of the following, but if I were you I would check these components in this order:

Your rear quick release. If this is too loose it can creak or click. This is especially true for newer external cam (aka exposed cam) quick releases. This is the case more than you would expect and requires no tools to fix. For the external cam QR type you might want to put a couple drops of lube on the moving parts to reduce friction. If it's an internal cam type QR, just make sure it's tight.

Your crank arms. If they are not properly tightened or greased, they can also make noise. If they are especially loose you can ruin them or they can fall off while you're riding (but this is also true for any part), so make sure they're tight.

Your pedals. Sometimes even when properly tensioned you will get a minor click from pedals. Make sure they're well greased and tightened to spec.

Your chainring bolts. Same deal. Make sure they're tight and greased or loc-tighted.

There are other potential issues but the ones listed above are the most likely culprits that are most closely related to the drivetrain.

There is no better place to turn when faced with a creak, click or clunk than Sheldon Brown.

Does the creaking only occur when you are pedalling on the bike, or can you recreate by lifting the back wheel and pedalling with your hand?

Creaking under load is often simply a bottom bracket that has not been fully tightened. As the bike is new and it uses a cartridge bb this could be likely so I'd check JM2's suggestions and if none of those work then take it back to the shop where you purchased it and explain the sound to them, they should be able to identify and rectify it relatively quickly (a bottom bracket requires a special tool).

Thanks for the suggestions :) I looked at the chain today while driving (not the best idea, but the road was empty), and the chain doesn't look like it's goint smoothly... It's not going in a straight line but moves about a half cm left-right while pedaling.
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StevenJul 6 '13 at 16:34

The sound is coming from the crankset area, so I guess it can't be the cassette? It happens on all three chainrings, and visually I don't see them bent
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StevenJul 6 '13 at 18:22

It could be that the chain has been bent. Are you familiar with the concept of chain crossing? This is when you use gear combinations such as the the smallest cog on the rear cassette and the smallest on the front. Doing this puts a lot of lateral force on the chain and can bend some links. It causes a noisy drive train, ghost shifts and the chain jumping off. It's a common mistake by new riders. The gear ratios you achieve by chain crossing can be usually in the middle chain ring and are more efficient there.
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DWGKNZJul 6 '13 at 19:17

I experienced the same condition of having a "clicking" noise that seemed to be coming from the bottom bracket/crank arm area. I too always keep my chain clean an lubed. Removing the chain and turning the crank arms quieted the clicking noise. I inspected the chain and determined that there was a suspect link or two in the same spot. I bought a new chain, cleaned and lubed it, installed it and the clicking noise was gone. An easier fix than if it had been the bottom bracket or a chain arm that was the problem. You may want to try the same type of repair.